Exact Solutions for Gravity-Segregated Flows in Porous Media
The review is devoted to exact analytical solutions for quasi-2D gravity segregated flows or gravity currents in subterranean porous formations. The problems under consideration are quasi-linear. The driving forces are two components of the buoyancy—one exerting the bulk of the light fluid and one d...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/14/2455 |
| _version_ | 1797417218389049344 |
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| author | Pavel Bedrikovetsky Sara Borazjani |
| author_facet | Pavel Bedrikovetsky Sara Borazjani |
| author_sort | Pavel Bedrikovetsky |
| collection | DOAJ |
| description | The review is devoted to exact analytical solutions for quasi-2D gravity segregated flows or gravity currents in subterranean porous formations. The problems under consideration are quasi-linear. The driving forces are two components of the buoyancy—one exerting the bulk of the light fluid and one due to the curvilinearity of the interface between the fluids. In the case of homogeneous formation or where the seal slope is negligible, the transport equation is parabolic and allows for a wide set of self-similar solutions. In a large-scale approximation of the buoyancy domination, the governing equation is hyperbolic; the method of characteristics allows for a detailed analytical description of gravity current propagation with final accumulation in the geological trap. Analytical models for leakage via the caprock seal are also discussed. The work was completed by formulating some unsolved problems in segregated flows in porous media. |
| first_indexed | 2024-03-09T06:15:37Z |
| format | Article |
| id | doaj.art-6836019fbcf34946aaa3a6aa33dfbdab |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T06:15:37Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6836019fbcf34946aaa3a6aa33dfbdab2023-12-03T11:53:45ZengMDPI AGMathematics2227-73902022-07-011014245510.3390/math10142455Exact Solutions for Gravity-Segregated Flows in Porous MediaPavel Bedrikovetsky0Sara Borazjani1Australian School of Petroleum and Energy Resources, The University of Adelaide, Adelaide, SA 5000, AustraliaAustralian School of Petroleum and Energy Resources, The University of Adelaide, Adelaide, SA 5000, AustraliaThe review is devoted to exact analytical solutions for quasi-2D gravity segregated flows or gravity currents in subterranean porous formations. The problems under consideration are quasi-linear. The driving forces are two components of the buoyancy—one exerting the bulk of the light fluid and one due to the curvilinearity of the interface between the fluids. In the case of homogeneous formation or where the seal slope is negligible, the transport equation is parabolic and allows for a wide set of self-similar solutions. In a large-scale approximation of the buoyancy domination, the governing equation is hyperbolic; the method of characteristics allows for a detailed analytical description of gravity current propagation with final accumulation in the geological trap. Analytical models for leakage via the caprock seal are also discussed. The work was completed by formulating some unsolved problems in segregated flows in porous media.https://www.mdpi.com/2227-7390/10/14/2455exact solutionsgravity segregated flowporous mediaself-similar solution |
| spellingShingle | Pavel Bedrikovetsky Sara Borazjani Exact Solutions for Gravity-Segregated Flows in Porous Media Mathematics exact solutions gravity segregated flow porous media self-similar solution |
| title | Exact Solutions for Gravity-Segregated Flows in Porous Media |
| title_full | Exact Solutions for Gravity-Segregated Flows in Porous Media |
| title_fullStr | Exact Solutions for Gravity-Segregated Flows in Porous Media |
| title_full_unstemmed | Exact Solutions for Gravity-Segregated Flows in Porous Media |
| title_short | Exact Solutions for Gravity-Segregated Flows in Porous Media |
| title_sort | exact solutions for gravity segregated flows in porous media |
| topic | exact solutions gravity segregated flow porous media self-similar solution |
| url | https://www.mdpi.com/2227-7390/10/14/2455 |
| work_keys_str_mv | AT pavelbedrikovetsky exactsolutionsforgravitysegregatedflowsinporousmedia AT saraborazjani exactsolutionsforgravitysegregatedflowsinporousmedia |